MMM LXX

Image Details

The above image is a detail from a nebulabrot rendering based on the fractal shown in MMM XLVII. In this case, an initial point \(w\) in the complex plane was selected. We set \(z_0 = w^{-1}\) (so that \(zw=1\)), then iterated the function \(z_{n+1} = z_n^7 + z_0\). If the number of iterations required in order for an orbit to escape was within a certain range, the orbit of the point was “exposed.” In this case, the image consists of three layers, with orbits escaping in 10 to 50 iterations, 50 to 250 iteration, and 250 to 1250 iterations.

A total of approximately 700 million exposures were made, for a total render time of about 3 days (this was somewhat parallelized—each of the layers was rendered on a separate core, and so the actual render time took as long as the most difficult to render layer; about 36 hours).

After processing the image, I noticed that the region shown above looked a bit like a skull sitting on an altar of candles (pareidolia, anyone?). Perhaps it would be better for Día de Muertos, but that is months away, and the image was ready to go this morning. ;)

The full-sized image is, if you ask me, also quite stunning. It is a bit large (23 MB), but worth it. Click the thumbnail above to see it.